2. To better understand the meaning behind poles and zeros, generate a mesh plot

Question

2. To better understand the meaning behind poles and zeros, generate a mesh plot in Matlab of the transfer function G(s) defined below using the skeleton code provided. Note that s is complex number and is given by s=+ja. You need to take the absolute value of the result because Matlab can't plot complex numbers G(s) = (s+15)(s2 + 100) HW #2 (Due Feb 14, 2018) ENME462: Vibrations, Controls, and Optimization II (Spring 2018) [sigma, omega] = meshgrid (-20:0.5:20); N = numerator of transfer function in terms of sigma , omega and j D = denominator of transfer function in terms of sigma , omega and j G = abs (N. /D); mesh (sigma, omega, G) a. b. c. Calculate the pole and zero locations of the transfer function G. Provide the mesh output (label axes). Identify the pole and zero locations on the plot. Does this make sense?

Explanation / Answer

The matlab code is provided below, I have plotted all the required data, you can conclude the results out of it.

------------------------------------------------------------------------------------------------

clc;clear all;
[sigma,omega]=meshgrid(-20:0.5:20);

N=sigma+omega*1j+10;
D=(sigma+omega*1j+15)*((sigma+1j*omega)^2+100);
G=abs(N./D);
mesh(sigma,omega,G);
xlabel('sigma','FontSize',18);ylabel('omega','FontSize',18);zlabel('G(s)','FontSize',18)

b=[1 10]; % coefficients of numerator
a=[1 15 100 1500]; % coefficients of denominator
fvtool(b,a,'polezero');
[b,a] = eqtflength(b,a);
% Obtaining zeros and poles from transfer function
[z,p,k] = tf2zp(b,a)
text(real(z)+.1,imag(z),'Zero')
text(real(p)+.1,imag(p),'Pole')

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.